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 Mat. Sb. (N.S.), 1988, Volume 136(178), Number 3(7), Pages 384–395 (Mi msb1749)

Asymptotics as $t\to0$ for solutions of the heat equation in a domain with a conical point

V. A. Kozlov

Abstract: The Dirichlet problem is considered for a second-order parabolic equation in a domain with a conical point on the boundary. The right sides need not satisfy consistency conditions at the initial time. A complete asymptotic expansion as $t\to0$ is obtained; it is uniform with respect to the space variables.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 383–395

Bibliographic databases:

UDC: 517.9
MSC: 35K05, 35B40

Citation: V. A. Kozlov, “Asymptotics as $t\to0$ for solutions of the heat equation in a domain with a conical point”, Mat. Sb. (N.S.), 136(178):3(7) (1988), 384–395; Math. USSR-Sb., 64:2 (1989), 383–395

Citation in format AMSBIB
\Bibitem{Koz88} \by V.~A.~Kozlov \paper Asymptotics as $t\to0$ for solutions of the heat equation in a domain with a conical point \jour Mat. Sb. (N.S.) \yr 1988 \vol 136(178) \issue 3(7) \pages 384--395 \mathnet{http://mi.mathnet.ru/msb1749} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=959489} \zmath{https://zbmath.org/?q=an:0699.35020} \transl \jour Math. USSR-Sb. \yr 1989 \vol 64 \issue 2 \pages 383--395 \crossref{https://doi.org/10.1070/SM1989v064n02ABEH003315} 

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This publication is cited in the following articles:
1. Artjom V. Sokirko, Keith B. Oldham, “The voltammetric response of a conical electrode”, Journal of Electroanalytical Chemistry, 430:1-2 (1997), 15
2. van den Berg M., Gilkey P., Kirsten K., Kozlov V.A., “Heat Content Asymptotics for Riemannian Manifolds with Zaremba Boundary Conditions”, Potential Anal., 26:3 (2007), 225–254
3. S. P. Degtyarev, “The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a conical point”, Sb. Math., 201:7 (2010), 999–1028
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